Euclid's Elements of Geometry |
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Page 25
... twice as many right angles , deducting four , as the figure hath sides . E A D B O For assume a point F within the figure , and draw the right lines FA , FB , FC , FD and FE . There are as many triangles con- structed as the figure has ...
... twice as many right angles , deducting four , as the figure hath sides . E A D B O For assume a point F within the figure , and draw the right lines FA , FB , FC , FD and FE . There are as many triangles con- structed as the figure has ...
Page 41
... twice a minus one a . Similarly a xa xbx c is similar to a2bc , by which is meant a multiplied by a multiplied by 6 multiplied by c ; likewise a 2a 62 indicates a2 x Nax 62. When we write ( a + b ) 2 it indicates the square of a + b ...
... twice a minus one a . Similarly a xa xbx c is similar to a2bc , by which is meant a multiplied by a multiplied by 6 multiplied by c ; likewise a 2a 62 indicates a2 x Nax 62. When we write ( a + b ) 2 it indicates the square of a + b ...
Page 46
... twice the rectangle under the parts . с K D A O B O F On AB describe the square ACDB , and draw CB , and from O draw OK parallel to AC , and cutting CB in G , and through G draw EF parallel to AB . The square ACDB , is equal to the ...
... twice the rectangle under the parts . с K D A O B O F On AB describe the square ACDB , and draw CB , and from O draw OK parallel to AC , and cutting CB in G , and through G draw EF parallel to AB . The square ACDB , is equal to the ...
Page 47
... twice the rectangle under the parts . OTHERWISE . The square of AB is equal to the sum of the rect- angles under AB and AO , and under AB and BO , ( by Prop . 2 , B. 2 , ) but the rectangle under AB and AO , is equal to the sum of the ...
... twice the rectangle under the parts . OTHERWISE . The square of AB is equal to the sum of the rect- angles under AB and AO , and under AB and BO , ( by Prop . 2 , B. 2 , ) but the rectangle under AB and AO , is equal to the sum of the ...
Page 48
... twice the rectangle under CD and DB together with the square of DB ; add to both the square of CD , and the rectangle under AD and DB together with the square of CD , is equal to twice the rectangle under CD and DB , together with the ...
... twice the rectangle under CD and DB together with the square of DB ; add to both the square of CD , and the rectangle under AD and DB together with the square of CD , is equal to twice the rectangle under CD and DB , together with the ...
Other editions - View all
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington No preview available - 2018 |
Euclid's Elements of Geometry: Translated From the Latin of ... Thomas ... Thomas Elrington No preview available - 2022 |
Euclid's Elements of Geometry: Translated from the Latin of ... Thomas ... Thomas Elrington No preview available - 2015 |
Common terms and phrases
absurd AC and CB AC by Prop AC is equal angle ABC angles by Prop arch base bisected centre circumference CKMB co-efficient Const contained in CD contained oftener divided divisor double draw drawn equal angles equal by Constr equal by Hypoth equal by Prop equal to twice equation equi equi-multiples equi-submultiples equiangular equilateral external angle fore four magnitudes proportional given angle given circle given line given right line given triangle gonal half a right inscribed less multiplying oftener contained parallel parallelogram perpendicular PROPOSITION quantities rectangle under AC rectilineal figure remaining angles remaining side right angles right line AC Schol segment side AC similar similarly demonstrated squares of AC submultiple subtract THEOREM tiple touches the circle triangle BAC twice the rectangle
Popular passages
Page 18 - If two triangles have two sides of the one equal to two sides of the...
Page 28 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 207 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 216 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 127 - In any proportion, the product of the means is equal to the product of the extremes.
Page 161 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Page 112 - To reduce fractions of different denominators to equivalent fractions having a common denominator. RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Page 213 - ... are to one another in the duplicate ratio of their homologous sides.
Page 163 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Page 88 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.